# Synergizing Transport-Based Generative Models and Latent Geometry for Stochastic Closure Modeling

arXiv: https://arxiv.org/abs/2602.17089 · HTML: https://mlsanity.com/paper/2602.17089/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 40 of its 89 references that are in the map.
- First posted on arXiv 19 Feb 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 40)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Quality](https://mlsanity.com/paper/2202.05830/) (2022)
- [Flow Matching in Latent Space](https://mlsanity.com/paper/2307.08698/) (2023)
- [Joint Training of a Convolutional Network and a Graphical Model for Human Pose Estimation](https://mlsanity.com/paper/1406.2984/) (2014)
- [Topological Autoencoders](https://mlsanity.com/paper/1906.00722/) (2019)
- [Don't Blame the ELBO! A Linear VAE Perspective on Posterior Collapse](https://mlsanity.com/paper/1911.02469/) (2019)
- [Refusion: Enabling Large-Size Realistic Image Restoration with Latent-Space Diffusion Models](https://mlsanity.com/paper/2304.08291/) (2023)
- [Probabilistic Forecasting with Stochastic Interpolants and F"ollmer Processes](https://mlsanity.com/paper/2403.13724/) (2024)
- [CoCoGen: Physically-Consistent and Conditioned Score-based Generative Models for Forward and Inverse Problems](https://mlsanity.com/paper/2312.10527/) (2023)
- [Earth System Modeling 2.0: A Blueprint for Models That Learn From Observations and Targeted High-Resolution Simulations](https://mlsanity.com/paper/1709.00037/) (2017)
- [Enforcing Statistical Constraints in Generative Adversarial Networks for Modeling Chaotic Dynamical Systems](https://mlsanity.com/paper/1905.06841/) (2019)
- [Joint Training of Variational Auto-Encoder and Latent Energy-Based Model](https://mlsanity.com/paper/2006.06059/) (2020)
- [Bayesian Conditional Diffusion Models for Versatile Spatiotemporal Turbulence Generation](https://mlsanity.com/paper/2311.07896/) (2023)
- [Sparse identification of nonlinear dynamics and Koopman operators with Shallow Recurrent Decoder Networks](https://mlsanity.com/paper/2501.13329/) (2025)
- [Alias-Free Latent Diffusion Models: Improving Fractional Shift Equivariance of Diffusion Latent Space](https://mlsanity.com/paper/2503.09419/) (2025)
- [Learning About Structural Errors in Models of Complex Dynamical Systems](https://mlsanity.com/paper/2401.00035/) (2023)

## Built on by (most cited first, 1 of 1)

- [Flow Learners for PDEs: Toward a Physics-to-Physics Paradigm for Scientific Computing](https://mlsanity.com/paper/2604.07366/) (2026)

## Abstract (arXiv)

Diffusion models recently developed for generative AI tasks can produce high-quality samples while still maintaining diversity among samples to promote mode coverage, providing a promising path for learning stochastic closure models. Compared to other types of generative AI models, such as GANs and VAEs, the sampling speed is known as a key disadvantage of diffusion models. By systematically comparing transport-based generative models on a numerical example of 2D Kolmogorov flows, we show that flow matching in a lower-dimensional latent space is suited for fast sampling of stochastic closure models, enabling single-step sampling that is up to two orders of magnitude faster than iterative diffusion-based approaches. To control the latent space distortion and thus ensure the physical fidelity of the sampled closure term, we compare the implicit regularization offered by a joint training scheme against two explicit regularizers: metric-preserving (MP) and geometry-aware (GA) constraints. Besides offering a faster sampling speed, both explicitly and implicitly regularized latent spaces inherit the key topological information from the lower-dimensional manifold of the original complex dynamical system, which enables the learning of stochastic closure models without demanding a huge amount of training data.